Answer:
Taylor sold 42 pizzas
Step-by-step explanation:
Make a system of equations where t represents the number of pizzas Taylor sold and j represents the number that Jeff sold:
t + j = 126
j = 2t
We can solve this system by substitution, since we can substitute 2t as j.
t + j = 126
t + 2t = 126
3t = 126
t = 42
Taylor sold 42 pizzas.
Answer:
Step-by-step explanation:
Let x represent the number of pizzas that Tailor sold.
Let y represent the number of pizzas that Jeff sold.
Together they have sold a total of 126 pizzas. This means that
x + y = 126- - - - - - - - -1
Taylor has sold half as many
pizzas as Jeff. This means that
x = 1/2 × y = y/2
Substituting x = y/2 into equation 1, it becomes
y/2 + y = 126
Multiplying both sides of the equation by 2, it becomes
y + 2y = 252
3y = 252
y = 252/3
y = 84
x = y/2 = 84/2
x = 42
Taylor sold 42 pizzas
4x ≤12 dimplify solve for x
Answer:
x<3
Step-by-step explanation:
Answer:
[tex]\boxed{x\leq 3}[/tex]
Step-by-step explanation:
[tex]4x \leq 12[/tex]
[tex]\sf Divide \ both \ parts \ by \ 4.[/tex]
[tex]\displaystyle \frac{4x}{4} \leq \frac{12}{4}[/tex]
[tex]x\leq 3[/tex]
2 lines connect to form a right angle. A third line extends between the 2 lines to form 2 angles which are labeled 1 and 2. Angles 1 and 2 are complementary and congruent. What is the measure of angle 1? 30° 45° 50° 75°
Answer:
the correct answer is 45°
Answer:
45 degrees.
Explanation: This is the correct answer on Edge 2021, just took the Unit test and made a 100%. Hope this helps ^-^.
2| x-3| - 5 = 7 Helpp
Answer:
x = {9, -3}
Step-by-step explanation:
2| x-3| - 5 = 72| x-3| = 12| x-3| = 6x - 3 = ± 6 ⇒ x= 3+ 6= 9⇒ x= 3 - 6= -3Or it can be shown as:
x= {9, -3}Determine if the field Bold Upper F equals 10 yz Bold i plus 10 xz Bold j plus 10 xy Bold k is conservative or not conservative.
F is conservative if we can find a scalar funciton f such that grad(f) = F.
This would entail
[tex]\dfrac{\partial f}{\partial x}=10yz[/tex]
[tex]\dfrac{\partial f}{\partial y}=10xz[/tex]
[tex]\dfrac{\partial f}{\partial z}=10xy[/tex]
Integrate both sides of the first equation with respect to x :
[tex]f(x,y,z)=10xyz+g(y,z)[/tex]
Differentiate both sides with respect to y :
[tex]\dfrac{\partial f}{\partial y}=10xz=10xz+\dfrac{\partial g}{\partial y}[/tex]
[tex]\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)[/tex]
Differentiate both sides with respect to z :
[tex]\dfrac{\partial f}{\partial z}=10xy=10xy+\dfrac{\mathrm dh}{\mathrm dz}[/tex]
[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C[/tex]
So we have
[tex]f(x,y,z)=10xyz+C[/tex]
that satisfies
[tex]\nabla f(x,y,z)=\mathbf F(x,y,z)[/tex]
and so F is indeed conservative.
the substitution method solve 6x-y=3 4x+3y=1
Answer:
[tex]( \frac{5}{11} \:, - \frac{3}{11} )[/tex]Step-by-step explanation:
6x - y = 3
4x + 3y = 1
Solve the equation for y
y = -3 + 6x
4x + 3y = 1
Substitute the given value of y into the equation
4x + 3y = 1
plug the value
[tex]4x + 3( - 3 + 6x) = 1[/tex]
Distribute 3 through the parentheses
[tex]4x - 9 + 18x = 1[/tex]
Collect like terms
[tex]22x - 9 = 1[/tex]
Move constant to R.H.S and change its sign
[tex]22x = 1 + 9[/tex]
Calculate the sum
[tex]22x = 10[/tex]
Divide both sides of the equation by 22
[tex] \frac{22x}{22} = \frac{10}{22} [/tex]
Calculate
[tex]x = \frac{5}{11} [/tex]
Now, substitute the given value of x into the equation
y = -3 + 6x
[tex]y = - 3 + 6 \times \frac{5}{11} [/tex]
Solve the equation for y
[tex]y = - \frac{3}{11} [/tex]
The possible solution of the system is the ordered pair ( x , y )
[tex](x ,\: y) = ( \frac{5}{11} ,\: - \frac{3}{11} )[/tex]-----------------------------------------------------------
Check if the given ordered pair is the solution of the system of equations
[tex]6 \times \frac{5}{11} - ( - \frac{3}{11} ) = 3[/tex]
[tex]4 \times \frac{5}{11 } + 3 \times ( - \frac{3}{11} ) = 1[/tex]
Simplify the equalities
[tex] 3 = 3[/tex]
[tex]1 = 1[/tex]
Since all of the equalities are true , the ordered pair is the solution of the system
[tex]( \: x ,\: y \: ) = ( \frac{5}{11} \:, - \frac{3}{11} )[/tex]Hope this helps..
Best regards!!
13. How long will a man take to cover
a distance of 7 kilometres by
walking 4 kilometres per hour?
(a) 1 hr. 35mins.
b) 1hr. 45mins
(c) Less than 1hr
(d) Exactly 1 hr.
(e) More than 2hrs
7km/ 4km per hour = 1 3/4 hours
3/4 hour = 45 minutes
Total time = 1 hour and 45 minutes.
About 30% of babies born with a certain ailment recover fully. A hospital is caring for five babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a bnomial experiment. If it is identify a success, specify the values of n,p, and q and list the possible values of hte random variable x.
1. Specigy the value of n. Select the correct choice bellow and fill in any answer boxes in your choice.
A. n=
B. This is not a binomial experiment
2. Specify the value of p. Select the correct choice below and fill in any answer boxes in your choice
A p=
B. This is not a binomial experiment.
3. Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice.
A. q=
B. This is not a binomial experiment
Answer:
n = 5 (a)p = 0.3 (a)q = 0.7 (a)Step-by-step explanation:
From the Given data in the above question it can be said that the experiment is a Binomial experiment because there is a success rate and a failure rate involved and the success rate is about 30% of the babies recovering from the ailment while the failure rate is about 70% of the babies not recovering from the ailment
The number of babies (n) = 5
success rate (p) = 30% = 0.3
failure rate (q) = 100% - 30% = 70% = 0.7
The possible values of the random value x = from 0 to 5
PLEASE HELP WILL GIVE EVERYTHING Amare wants to ride a Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. It takes six minutes to do three revolutions on the Ferris wheel. Complete the function, h(t), which models Amare's height above the ground, in meters, as a function of time, t, in minutes. Assume he enters the ride at the low point when t = 0.
Answer:
[tex]h(t)=-25\cos(\pi t)+29[/tex]
Step-by-step explanation:
First thing to understand is that we will be producing a sine or cosine function to solve this one. I'll use a cosine function for the sake of the problem, since it's most easily represented by a cosine wave flipped over. If you're interested in seeing a visualization of how a circle's height converts to one of these waves, you may find the Better Explained article Intuitive Understanding of Sine Waves helpful.
Now let's get started on the problem. Cosine functions generally take the form
[tex]y=a\cos(b(x-c))+d[/tex]
Where:
[tex]|a|[/tex] is the amplitude
[tex]\frac{2\pi}{b}[/tex] is the period, or the time it takes to go one full rotation around the circle (ferris wheel)
[tex]c[/tex] is the horizontal displacement
[tex]d[/tex] is the vertical shift
Step one, find the period of the function. To do this, we know that it takes six minutes to do three revolutions on the ferris wheel, so it takes 2 minutes to do one full revolution. Now, let's find [tex]b[/tex] to put into our function:
[tex]\frac{2\pi}{b}=2[/tex]
[tex]2\pi=2b[/tex]
[tex]\pi=b[/tex]
I skipped some of the basic algebra to shorten the solution, but we have found our b. Next, we'll get the amplitude of the wave by using the maximum and minimum height of the wheel. Remember, it's 4 meters at its lowest point, meaning its highest point is 54 meters in the air rather than 50. Using the formula for amplitude:
[tex]\frac{\max-\min}{2}[/tex]
[tex]\frac{54-4}{2}[/tex]
[tex]\frac{50}{2}=25=a[/tex]
Our vertical transformation is given by [tex]\min+a[/tex] or [tex]\max-a[/tex], which is the height of the center of the ferris wheel, [tex]4+25=29=d[/tex]
Because cosine starts at the minimum, [tex]c=0[/tex].
The last thing to point out is that a cosine wave starts at its maximum. For that reason, we need to flip the entire function by making the amplitude negative in our final equation. Therefore our equation ends up being:
[tex]h(t)=-25\cos(\pi t)+29[/tex]
Over what interval is the function in this graph increasing?
5
-6
-5
The following are the weekly amounts of welfare payments made by the federal government to a sample of six families: $139, $136, $130, $136, $147, and $136. What is the range
Answer:
$17
Step-by-step explanation:
data:
$139 $136 $130 $136 $147 $136In statistics, the range is the difference between the highest value and the lowest value of the data set.
Highest value = $147
Lowest value = $130
Range = $17
I need help for this problem!
Answer:
[tex] a = 2.7 [/tex]
Step-by-step explanation:
Distributive property can be used to solve the equation, by multiplying [tex] \frac{2}{3} [/tex] with [tex] 6a, [/tex] and [tex] 9 [/tex]
Thus,
[tex] (\frac{2}{3}*6a) + (\frac{2}{3}*9) = 16.8 [/tex]
[tex] 2*2a + 2*3 = 16.8 [/tex]
[tex] 4a + 6 = 16.8 [/tex]
Subtract 6 from both sides.
[tex] 4a + 6 - 6 = 16.8 - 6 [/tex]
[tex] 4a = 10.8 [/tex]
Divide both sides by 4 to solve for a
[tex] \frac{4a}{4} = \frac{10.8}{4} [/tex]
[tex] a = 2.7 [/tex]
In a large university, 20% of the students are business majors. A random sample of 100 students is selected, and their majors are recorded. a) Compute the standard error of the proportion. b) What is the probability that the sample contains at least 12 business majors
Answer:
a. 0.04
b. 0.9772
Step-by-step explanation:
Please check attachment for complete solution and step by step explanation
Which equation is graphed in the figure? A. 7y = 5x + 14 B. 7y = -5x + 14 C. 5y = -7x + 10 D. 5y = 7x + 10
Answer:
The answer is D. You can confirm this from the graph down below
Step-by-step explanation:
Subtracting polynomials
Answer:
The third side of the triangle is 10x + 3
Step-by-step explanation:
x + 1 + 2x + 4 = 3x + 5
( 13x + 8 ) - ( 3x + 5 ) = 13x + 8 - 3x - 5
= 10x + 3
By looking at the plots, Beth says that the two means are about 5 years apart. Which is true about Beth's statement?
She is correct because the medians are 10 years apart,
which means the means are half of that, or 5 years
apart
O She is correct because the maximum ages of the
pennies in each set are 5 years apart.
O She is not correct because the means are both equal to
02
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
12
O She may not be correct because means cannot be
determined from the box plots.
In the diagram of RST, which term describes point U?
A.
Circumcenter
B.
Centroid
C.
Incenter
D.
Orthocenter
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is C, Incenter.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
In a triangle, the point at which all the angle bisectors of the triangle meet is known as the Incenter.
Since In ΔRST, all the angles are bisected by the angle bisector, and the point at which all the angle bisectors meet is represented by U. Thus, it can be concluded that the point U represents the incenter of the triangle.
Learn more about Triangle:
https://brainly.com/question/2773823
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You work at a coffee house. Roasted coffee beans retain approximately 3/5 of their initial weight. Approximately what percent of their inital weight do they retain?
Answer:
60%
Step-by-step explanation:
We need convert 3/5 into a percent in order to find the answer.
We can convert by first dividing 3 by 5 to find the decimal value.
3/5= .6
Now we need to multiply by 100 to make it a percentage
.6 x 100= 60
60%
Suppose , varies jointly with g and v, and j = 2 when g = 4 and v= 3.
Find j when g = 8 and v= 11.
Answer:
j = 44/3
Step-by-step explanation:
j varies jointly as g and v. This can be represented mathematically as:
[tex]j \alpha gv\\j = kgv[/tex].............(1)
Where k is a constant of proportionality
j = 2 when g = 4 and v = 3
Substitute these values into equation (1)
2 = k * 4 * 3
2 = 12 k
k = 1/6
when g = 8 and v = 11:
j = (1/6) * 8 * 11
j = 44/3
find the total number of terms.32,256,2048,16384,......,2⁵⁰
Answer:
16 termsStep-by-step explanation:
32,256,2048,16384,......,2⁵⁰
32=2⁵
256=2⁸
2048=2¹¹
16384=2¹⁴
2⁵, 2⁸, 2¹¹,2¹⁴, ….,2⁵⁰
[tex]t_{1}[/tex]=2⁵; [tex]t_{2}[/tex]=2⁸
r=2⁸:2⁵=2³
[tex]t_{n}[/tex]=[tex]t_{1}[/tex]*[tex]r^{n-1}[/tex]
2⁵*[tex]2^{3(n-1)}[/tex] =2⁵⁰
5+3(n-1)=50
3n-3=45
3n=48
n=48:3
n=16
So, 16 terms
What is the range of the function (-1,2) (3,6) (5,8)
Answer:
Range { 2,6,8}
Step-by-step explanation:
The domain is the input and the range is the output
Range { 2,6,8}
Answer:
2, 6, 8
Step-by-step explanation:
The range is the possible values of y, (x, y). So in this case, y could be 2, 6, or 8.
1. find x and y 2. find the measure of each side of LMN
Answer:
X= 3
Y= 18
Each side of the triangle= 10 units
Step-by-step explanation:
LMN is equilateral so
LM = MN
3x+1= 4x-2
3x-4x = -2-1
-x = -3
X= 3
MP is the perpendicular bisector of line LN
so definitely angle lpm =90.
And lpm = 5y = 90
5y = 90
Y= 90/5
Y = 18°
For the side of the triangle
3x+1
But x= 3
3(3)+1
9+1
10
Each side of the triangle= 10 units
x varies directly as y, when x=4,y=3. find Y when x=5
Answer:
Y =4
Step-by-step explanation:
Hope it helps
Suppose that your uncle is decorating his house for christmas.He uses 300 strands of lights each containing 150 light bulbs.Each light bulb consumes 4 watts of power. If he illuminates his light for 5 hours a day for 30 days and power in his area sells for $0.08/kWh, how much will he end up paying to light his home for the holidays?
Answer:
$14.4
Step-by-step explanation:
From the question;
There are 300 strands of light each containing 150 light bulbs. Altogether, there are;
300 x 150 light bulbs = 45000 light bulbs.
Also;
Each bulb consumes 4 watts of power. Since there are 45000 light bulbs, the total power consumed by all the bulbs is;
45000 x 4 watts = 180000watts
Next convert the total power consumed to kW by dividing by 1000. i.e
180000watts = 180kW
Therefore, total power consumed is 180kW
He lights up for 5 hours a day for 30 days. This means that the total number of hours he lights his home for those 30 days is:
30 x 5 hours = 150 hours.
Now since power in his area sells for $0.08/kWh, this means that;
1kWh costs $0.08
Then;
180kWh will cost [180kWh x $0.08 / 1kWh] = $14.4
Therefore, he will end up paying $14.4 to light his home for the holidays.
Write the slip-intercept form of the equation of the line described
- through: (4,1), parallel to y = 5/6x - 3
- through: (3,3), perp. to y= -3/8x + 2
Answer:
1) y=⅚x -2⅓
2) y=8/3x -5
Step-by-step explanation:
Point-slope form:
y=mx+c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient.
Gradient of given line= [tex] \frac{5}{6} [/tex]
Thus, m=⅚
Susbt. m=⅚ into the equation,
y= ⅚x +c
Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.
When x=4, y=1,
1= ⅚(4) +c
[tex]1 = \frac{20}{6} + c \\ c = 1 - \frac{20}{6} \\ c = 1 - 3 \frac{1}{3} \\ c = - 2 \frac{1}{3} [/tex]
Thus the equation of the line is [tex]y = \frac{5}{6} x - 2 \frac{1}{3} [/tex].
The gradients of perpendicular lines= -1.
Gradient of given line= -⅜
-⅜(gradient of line)= -1
gradient of line
= -1 ÷ (-⅜)
= -1 ×(-8/3)
= [tex] \frac{8}{3} [/tex]
[tex]y = \frac{8}{3} x + c[/tex]
When x=3, y=3,
[tex]3 = \frac{8}{3} (3) + c \\ 3 = 8 + c \\ c = 3 - 8 \\ c = - 5[/tex]
Thus the equation of the line is [tex]y = \frac{8}{3} x - 5[/tex].
The linear combination method is applied to a system of equations as shown. 4(.25x + .5y = 3.75) → x + 2y = 15 (4x – 8y = 12) → x – 2y = 3 2x = 18
Answer:
x+2y=12-------(1)
x-2y=3---------(2)
Adding equations 1 and 2
we get
2x=18
x=9
Equation 1
9+2y=15
2y=15-9
2y=6
y=3
The solution of the given system is x=9, y=3
Step-by-step explanation
If cot(x)=2/3, what is The value of csc(x)
Answer:
Step-by-step explanation:
cot (x)=2/3
we know csc^2(x)-cot^2(x)=1
csc^2(x)=1+cot^2(x)=1+4/9=13/9
csc (x)=±√13/3
Determine the height of the tree to the nearest foot
Answer:
80 ft
Step-by-step explanation:
in similar triangles sides are proportional.
[tex]\frac{176}{h} =\frac{120+100}{100} =\frac{220}{100} =\frac{22}{10} \\h=\frac{10}{22} \times 176=80[/tex]
h=80 ft
A city's population is currently 50,000. If the population doubles every 70 years, what will the population be 280 years from now?
Answer:
200,000
Step-by-step explanation:
The current population: 50,000
Doubling time:70
Population after 280 years=?
280/70=4
50,000*4=200,000
Hope this helps ;) ❤❤❤
Answer: 800,000
Step-by-step explanation: 50,000x2=100,000. That is after 70 years. 100,000x2=200,000. This is after 140 years. 200,000x2=400,000. This is after 210 years. 400,000x2=800,000. This is after 280 years.
Find the common difference of the arithmetic sequence. 4, 10, 16, 22, . . .
Answer:
6
Step-by-step explanation:
10 - 4 = 6
16 - 10 = 6
22 - 16 = 6
Answer:6
Step-by-step explanation:
1) 10-4=6
2) 16-10=6
3) 22-16=6
i will give brainliest and 50 points pls help ASP
Answer:
2064 cm squared
Step-by-step explanation:
First I will try to solve for the area of each side:
Side #1(trapezoid): Area of a Trapezoid = half of sum of bases*height
A= (6+27)/2*8 = 33/2 *8 =132
Side #2(opposite trapezoid): Same area as theother one...
A= 132
Side#3(Top):
A=6*30=180
Side #4(Bottom):
A=27*30=810
Side #5(Left side):
A=10*30=300
Side #6(Right Side):
A=30*17=510
After solving for all the areas we just need to add them all up:
SA=132+132+180+810+300+510=2064 cm squared
Hope this helps!
Answer:
total surface area = 2064 cm^2
Step-by-step explanation:
Given prism with trapezoidal bases.
H=8
B1 = 27
B2 = 6
slant sides = 10, 17 cm
H = 30
Area of bases
A1 = 2 * (B1+B2)/2 * h
= 2* ( (27+6)/2 * 8 )
= 264
Area of sides
A2 = perimeter * H
= (6+17+27+10)*30
= 1800
Total area = A1+A2 = 264+1800 = 2064 cm^2